Too numerous to list here. This site (http://www.howtocreate.co.uk/ie8.html) is by one of my favorite testers. So far, it looks like IE8 will continue to be at least 10 years behind web standards.

The advances have mostly been in the CSS support, which has actually moved IE forward towards the other browsers. It has made a substantial advance through CSS 2.1, though is still behind the others in terms of CSS 3.

Unfortunately, there are almost no advances at all in DOM support, and IE remains nearly a decade behind the other browsers.